Generalized majority rules: utilitarian welfare in large but finite populations

Generalized majority rules are electoral rules in which an alternative needs to obtain a fixed percentage (not necessarily 50%) of all votes in order to win. While Krishna and Morgan (Am Econ J Microeconom 7:339–375, 2015) demonstrate that simple majority maximizes expected utilitarian welfare for limiting populations regardless of the prior support for the alternatives, this paper finds that, when the prior support is known, a continuum of voting rules also achieves the same welfare. Moreover, as the population approaches the limit, every voting rule eventually becomes welfare inferior to picking the ex-ante majority without an election. Examining the properties of these optimal rules allows us to generalize the relationship between voter participation and welfare beyond the symmetric case.